The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite… (More)

In this paper we prove that if a weight w satisfies the C q condition, then the Lp(w) norm of a one-sided singular integral is bounded by the Lp(w) norm of the one-sided Hardy-Littlewood maximal… (More)

In this paper we give sufficient conditions on pair of weights (w, v) for some one-sided operators to be bounded from Lp(vp) to Lp(wp). The operators we deal with include the one-sided fractional… (More)

Only the position representation is used in introductory quantum mechanics and the momentum representation is not usually presented until advanced undergraduate courses. To emphasize the relativity… (More)

The quantization of the electromagnetic field in vacuum is presented without reference to lagrangean quantum field theory. The equal time commutators of the fields are calculated from basic… (More)

Position and momentum of a particle can take any value in a continuous spectrum ; these values are independent but their indeterminacies are correlated; momentum and position are mutually the… (More)

Recent results about the slow dynamics present in a fully developed turbulent flow are reported. In a previous paper [de la Torre & Burguete, 2007] we showed that the mean velocity field in a… (More)